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Wave Equations on Unbounded Domains

Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 50)

Keywords

Wave Equation Wave Train Unbounded Domain Secular Term Progressive Wave 
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14.7 Guide to the Literature

  1. 1.
    Ablowitz, M.J. and Benney, D.J. (1970), The evolution of multi-phase modes for nonlinear dispersive waves, Stud. Appl. Math. 49, pp. 225–238.zbMATHGoogle Scholar
  2. 11.
    Benney, D.J. and Newell, A.C. (1967), The propagation of nonlinear wave envelopes, J. Math. Phys. 46, pp. 133–139.zbMATHMathSciNetGoogle Scholar
  3. 19.
    Bourland, F.J. and Haberman, R. (1989), The slowly varying phase shift for perturbed, single and multi-phased strongly nonlinear dispersive waves, Physica 35D, pp. 127–147.MathSciNetGoogle Scholar
  4. 28.
    Chikwendu, S.C. and Kevorkian, J. (1972), A perturbation method for hyperbolic equations with small nonlinearities, SIAM J. Appl. Math. 22, pp. 235–258.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 29.
    Chikwendu, S.C. and Easwaran, C.V. (1992), Multiple scale solution of initial-boundary value problems for weakly nonlinear wave equations on the semiinfinite line, SIAM J. Appl. Math. 52, pp. 946–958.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 36.
    de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.Google Scholar
  7. 73.
    Haberman, R. and Bourland, F.J. (1988), Variation of wave action: modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation, Physica D 32, pp. 72–82.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 104.
    Kevorkian, J.K. and Cole, J.D. (1996), Multiple Scale and Singular Perturbation Methods, Springer-Verlag, New York.zbMATHGoogle Scholar
  9. 126.
    Luke, J.C. (1966), A perturbation method for nonlinear dispersive wave problems, Proc. R. Soc. London Ser. A, 292.Google Scholar
  10. 134.
    McLaughlin, D.W. and Scott, A.C. (1978), Perturbation analysis of fluxon dynamics, Phys. Rev. A 18, pp. 1652–1680.CrossRefGoogle Scholar
  11. 167.
    Scott, A. (1999), Nonlinear Science: Emergence and Dynamics of Coherent Structures, Oxford University Press, Oxford.zbMATHGoogle Scholar
  12. 193.
    Van der Burgh, A.H.P. (1979), On the asymptotic validity of perturbation methods for hyperbolic differential equations, in Asymptotic Analysis, from Theory to Application (Verhulst, F., ed.) Lecture Notes in Mathematics 711, pp. 229–240, Springer-Verlag, Berlin.Google Scholar
  13. 219.
    Whitham, G.B. (1970), Two-timing, variational principles and waves, J. Fluid. Mech. 44, pp. 373–395.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 220.
    Whitham, G.B. (1974), Linear and Nonlinear Waves, John Wiley, New York.zbMATHGoogle Scholar

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© Springer Science+Business Media, Inc. 2005

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